Switching power supplies or switching power converters are used in a variety of applications to convert power from an input source to drive a load. Control of the conversion is provided by pulse width modulation of power supply switches, for example, by varying a switch on time or duty cycle, with the converter operating at a given switching frequency. Switching power supplies may be operated using constant current (CC) control techniques for improved reliability to allow the power supply to continue provision of output current beyond a nominal value, and constant voltage (CV) operation is used at lower power levels, with some power supplies employing constant power (CP) operation. Constant voltage operation is sometimes achieved using a voltage loop to regulate the output voltage and constant current operation is sometimes achieved using a current loop to regulate the output current. The voltage loop is often used for constant power operation with a power supply controller operating the voltage loop with a voltage reference set to the maximum power value divided by the output current. The use of constant current operation may allow the power supply to avoid overcurrent protection shutdown in certain situations. This is advantageous, for example, when using multiple power supplies in a redundant system. Without constant current control capabilities, a given power supply could assume too much load current for some reason and hit overcurrent protection (OCP) levels to trigger a shutdown. This, in turn, may lead to another power supply assuming the current load, reaching OCP levels, and ultimately shutting down. Thus, constant current control using a voltage loop to regulate output voltage and a current loop to regulate output current is an important feature in certain applications, such as portable telecommunications devices, battery chargers, server applications, etc. However, these power supply control techniques suffer from potential voltage overshoot when control is switched from the current loop to the voltage loop. For instance, when a large load current is demanded during operation according to the current loop, the voltage loop may call for a large duty cycle when the output voltage is low relative to a voltage reference. Switching control back to the voltage loop may result in pulse width modulation according to a large duty cycle in excess of that needed to obtain the desired voltage, leading to a voltage spike or overshoot condition which can damage downstream equipment and/or cause the power supply to be shut down. Accordingly, improved power supply control techniques and apparatus are needed to mitigate or avoid voltage overshoot in switching from current loop control to voltage loop control.